This invention relates to a new cultivar of blackberry called ‘Driscoll Thornless Sleeping Beauty’. The new cultivar was developed from a spineless mutant of the patented cultivar ‘Sleeping Beauty’ (U.S. Plant Pat. No. 13,758 P3). ‘Sleeping Beauty’ was developed from a hybridization of the female cultivar ‘Brazos’ (unpatented) with the male cultivar ‘Hull Thornless’ (unpatented). The new variety was discovered in 2001 in a field of ‘Sleeping Beauty’ near Jacona, Mexico where after it was propagated to produce plants for planting trials in 2002. The new cultivar was selected in 2001 for its thornless canes. The cultivar has been asexually propagated in Mexico by hardwood cuttings and reproduced true to type plants.